Q.Which measure of dispersion is the best and how?

Each measure has strengths and weaknesses, but one is based on all the values, usable in advanced work and the foundation of the most-used relative measure.

Among the measures of dispersion, standard deviation is generally considered the best, for the following reasons:

1. Based on all observations. Unlike the range (only two values) or the quartile deviation (only the middle 50%), standard deviation uses every value, so it reflects the whole distribution.
2. Amenable to further treatment. It can be handled algebraically and is used extensively in more advanced statistical work (for example in comparing distributions and in the coefficient of variation).
3. Independent of origin. Its value does not change if a constant is added to or subtracted from every value.
4. Basis of the coefficient of variation. The most commonly used relative measure of dispersion, $C.V. = \dfrac{\sigma}{\bar{x}} \times 100$, is built on the standard deviation, allowing comparison across distributions with different units or averages.

Its main limitations are that it is comparatively difficult to compute and interpret, and that (like mean deviation) it cannot be calculated for open-ended distributions. Even so, because it is based on all values and is so widely applicable, standard deviation is regarded as the best measure of dispersion.